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A solution method for decomposing vector fields in Hamilton energy
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作者 Xin Zhao Ming Yi +2 位作者 zhou-chao wei Yuan Zhu Lu-Lu Lu 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第9期645-653,共9页
Hamilton energy,which reflects the energy variation of systems,is one of the crucial instruments used to analyze the characteristics of dynamical systems.Here we propose a method to deduce Hamilton energy based on the... Hamilton energy,which reflects the energy variation of systems,is one of the crucial instruments used to analyze the characteristics of dynamical systems.Here we propose a method to deduce Hamilton energy based on the existing systems.This derivation process consists of three steps:step 1,decomposing the vector field;step 2,solving the Hamilton energy function;and step 3,verifying uniqueness.In order to easily choose an appropriate decomposition method,we propose a classification criterion based on the form of system state variables,i.e.,type-I vector fields that can be directly decomposed and type-II vector fields decomposed via exterior differentiation.Moreover,exterior differentiation is used to represent the curl of low-high dimension vector fields in the process of decomposition.Finally,we exemplify the Hamilton energy function of six classical systems and analyze the relationship between Hamilton energy and dynamic behavior.This solution provides a new approach for deducing the Hamilton energy function,especially in high-dimensional systems. 展开更多
关键词 HAMILTON ENERGY DYNAMICAL systems VECTOR field EXTERIOR DIFFERENTIATION
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A class of two-dimensional rational maps with self-excited and hidden attractors
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作者 Li-Ping Zhang Yang Liu +2 位作者 zhou-chao wei Hai-Bo Jiang Qin-Sheng Bi 《Chinese Physics B》 SCIE EI CAS CSCD 2022年第3期224-233,共10页
This paper studies a new class of two-dimensional rational maps exhibiting self-excited and hidden attractors. The mathematical model of these maps is firstly formulated by introducing a rational term. The analysis of... This paper studies a new class of two-dimensional rational maps exhibiting self-excited and hidden attractors. The mathematical model of these maps is firstly formulated by introducing a rational term. The analysis of existence and stability of the fixed points in these maps suggests that there are four types of fixed points, i.e., no fixed point, one single fixed point, two fixed points and a line of fixed points. To investigate the complex dynamics of these rational maps with different types of fixed points, numerical analysis tools, such as time histories, phase portraits, basins of attraction, Lyapunov exponent spectrum, Lyapunov(Kaplan–Yorke) dimension and bifurcation diagrams, are employed. Our extensive numerical simulations identify both self-excited and hidden attractors, which were rarely reported in the literature. Therefore, the multi-stability of these maps, especially the hidden one, is further explored in the present work. 展开更多
关键词 two-dimensional rational map hidden attractors multi-stability a line of fixed points chaotic attractor
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Extremely hidden multi-stability in a class of two-dimensional maps with a cosine memristor
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作者 Li-Ping Zhang Yang Liu +3 位作者 zhou-chao wei Hai-Bo Jiang wei-Peng Lyu Qin-Sheng Bi 《Chinese Physics B》 SCIE EI CAS CSCD 2022年第10期331-340,共10页
We present a class of two-dimensional memristive maps with a cosine memristor. The memristive maps do not have any fixed points, so they belong to the category of nonlinear maps with hidden attractors. The rich dynami... We present a class of two-dimensional memristive maps with a cosine memristor. The memristive maps do not have any fixed points, so they belong to the category of nonlinear maps with hidden attractors. The rich dynamical behaviors of these maps are studied and investigated using different numerical tools, including phase portrait, basins of attraction,bifurcation diagram, and Lyapunov exponents. The two-parameter bifurcation analysis of the memristive map is carried out to reveal the bifurcation mechanism of its dynamical behaviors. Based on our extensive simulation studies, the proposed memristive maps can produce hidden periodic, chaotic, and hyper-chaotic attractors, exhibiting extremely hidden multistability, namely the coexistence of infinite hidden attractors, which was rarely observed in memristive maps. Potentially,this work can be used for some real applications in secure communication, such as data and image encryptions. 展开更多
关键词 two-dimensional maps memristive maps hidden attractors bifurcation analysis extremely hidden multi-stability
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